Vol. 24, No. 3, 1968

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Point-like 0-dimensional decompositions of S3

Howard Wilson Lambert and Richard Benjamin Sher

Vol. 24 (1968), No. 3, 511–518

This paper is concerned with upper semicontinuous decompositions of the 3-sphere which have the property that the closure of the sum of the nondegenerate elements projects onto a set which is 0-dimensional in the decomposition space. It is shown that such a decomposition is definable by cubes with handles if it is point-like. This fact is then used to obtain some properties of point-like decompositions of the 3-sphere which imply that the decomposition space is a topological 3-sphere. It is also shown that decompositions of the 3-sphere which are definable by cubes with one hole must be pointlike if the decomposition space is a 3-sphere.

Mathematical Subject Classification
Primary: 54.78
Received: 25 July 1966
Published: 1 March 1968
Howard Wilson Lambert
Richard Benjamin Sher